US 4990001 A Abstract A method of synthesizing drive systems, including dc, synchronous and asynchronous ac, and step motor drive systems, of instantaneous response and zero error in both transient and steady state with respect to an input command and of infinite disturbance rejection ratio with respect to a load torque changes, comprising an inner positive current feedback of exactly specified nature and value of its transfer function forcing the motor impedance to zero for load independence, and further comprising control functions in a direct path with respect to both position and velocity feedback loop and in a feedforward path of exactly specified values which, together with the inner positive current feedback loop, provide for the zero-dynamics system transfer function with respect to the command with an associated instantaneous response.
Claims(9) 1. A method for synthesizing electric motor drive system of infinite disturbance rejection ratio and zero dynamics comprising:
accepting a source of electrical energy of a constant voltage at an input to a power converter, coupling mechanically a shaft of an electric motor to a load to be driven at an output, controlling a power flow from said input to said output, modulating said power converter for the control of said power flow in a pulse width modulation manner, supplying a total control signal for modulating said power converter, supplying position feedback pulses, feeding back said position feedback pulses and comparing their frequency and phase with frequency and phase of position command pulses in a phase frequency detector in a negative feedback manner; thereby producing a position error voltage proportional to a difference in frequency and phase between said position command pulses and said position feedback pulses; supplying a position command obtained as a voltage potential, passing said position command through a position direct path circuit; thereby producing said position command pulses, passing said position command through a differentiation circuit; thereby producing a velocity signal voltage, passing said velocity signal voltage through a velocity direct path circuit; thereby producing a velocity command voltage, passing said velocity signal voltage through a feedforward circuit; thereby producing a feedforward signal, supplying a velocity feedback signal, feeding back said velocity feedback signal and summing it with said velocity command voltage and said position error voltage in a negative feedback manner; thereby producing a resulting error voltage, passing said resulting error voltage through a cascade connection of a stabilizing network and a control circuit; thereby producing a control signal proportional to the algebraic sum of said velocity command voltage and said velocity feedback signal and said position error voltage, sensing a current through said electric motor, feeding back the sensed current signal through a current feedback circuit in a positive feedback loop with respect to said control signal and said feedforward signal and summing the sensed current signal with said control signal and said feedforward signal, supplying said total control signal, obtained as the sum of said control signal and said feedforward signal and the current signal fed through said current feedback circuit, for modulating said power converter for the control of the flow of power from the input electrical source to the output mechanical load, whereby all electrical and mechanical time constants associated with said electric motor and with the mechanical load are brought to zero yielding an infinite disturbance rejection ratio by making an angular shaft position and speed independent of said load and yielding a zero dynamics by cancelling remaining time constants in the system and making a transfer function from said position command to said angular shaft position a constant and therefore of zero dynamics. 2. The method of claim 1 wherein said current feedback circuit in said positive feedback loop is synthesized using an equation providing transfer function in laplace domain of said current feedback circuit
H(s)=Z in said equation Z _{ekv} (s) being an impedance of said electric motor, R being a transresistance of a motor current sense device, A being a voltage gain of a pulse width modulation control and power stage, K being a voltage gain of a buffering differential amplifier, and s being a complex frequency laplace variable in the transfer function H(s).3. The method of claim 2 wherein said equation providing transfer function of said current feedback circuit is physically implemented, thereby implementing said current feedback circuit, in case of the direct current motors, or the alternating current synchronous motors, or the step motors, in accordance with an expression giving said impedance of said electric motor in laplace domain Z
_{ekv} (s) as a series connection of a resistance and an inductive reactance of said electric motor, and, in case of the alternating current asynchronous motors, in accordance with another expression giving said impedance of said electric motor in laplace domain A_{ekv} (s) as a series connection of a stator impedance with a parallel connection of a magnetizing reactance and a rotor impedance referred to stator of said electric motor.4. The method of claim 1 wherein said position direct path circuit is synthesized using an equation providing transfer function of said position direct path circuit
K in said equation m being a scaling constant equal to said transfer function from said position command to said angular shaft position, K _{e} being a gain constant of a digital encoder, and K_{g} being a gear ratio constant of a gear box.5. The method of claim 4 wherein said equation providing transfer function of said position direct path circuit is physically implemented, thereby implementing said position direct path circuit, as a constant gain circuit.
6. The method of claim 1 wherein said velocity direct path circuit is synthesized using an equation providing transfer function of said velocity direct path circuit
K in said equation m being a scaling constant equal to said transfer function from said position command to said angular shaft position, and K _{v} being a gain constant of a tach.7. The method of claim 6 wherein said equation providing transfer function of said velocity direct path circuit is physically implemented, thereby implementing said velocity direct path circuit, as a constant gain circuit.
8. The method of claim 1 wherein said feedforward circuit is synthesized using an equation providing transfer function of said feedforward circuit
K in said equation m being a scaling constant equal to said transfer function from said position command to said angular shaft position, K _{m} being a counter electromotive force constant characterizing production of a counter electromotive force proportional to said angular shaft speed of said electric motor, and A being a voltage gain of a pulse width modulation control and power stage.9. The method of claim 8 wherein said equation providing transfer function of said feedforward circuit is physically implemented, thereby implementing said feedforward circuit, as a constant gain circuit.
Description This invention relates to electric motor drive systems, including dc, synchronous and asynchronous ac, and step motor drive systems using an inner current feedback loop, both position and velocity feedback loops, and a direct-paths as well as a feedforward-path control functions to control the output angular position and velocity of the motor shaft when either a load torque or an input command changes by making the system of infinite disturbance rejection ratio and zero-dynamics/instantaneous response. In the field of drive systems it is of interest to minimize the effects of load changes as well as to follow an input command, in terms of either velocity or position, as close as possible in both transient and steady state and under all load conditions within the physical limitations of a system. Theoretically, both of these objectives may be achieved using a negative feedback control theory and employing an infinite gain in the loop. The problem encountered in such a case is that the system will necessarily become unstable so that, with this classical approach, no solution can be achieved. As a matter of fact, this remains a classical problem in system and control theory and practice. An infinite disturbance rejection ratio, i.e., load independence, has been achieved employing a positive feedback as described in the U.S. Pat. application No. 07/323,630, filed November 1988 and entitled "Synthesis of Load-Independent DC Drive System" by these same two inventors N. A. Losic and Lj. Dj. Varga, and in the U.S. patent application No. 07/316,664, February 1989, by N. A. Losic and Lj. Dj. Varg entitled "Synthesis of Load-Independent AC Drive Systems" and allowed for issuance December 1989. The inventions have been generalized and included synthesis of a load-independent step motor drive systems in a copending and coassigned application by Lj. Dj. Varga and N. A. Losic, "Synthesis of Zero-Impedance Converter" filed December 1989. Furthermore, a synthesis of drive systems of infinite disturbance rejection ratio and zero-order dynamics and without the use of position and velocity feedbacks is described in a copending and coassigned application by N. A. Losic and Lj. Dj. Varga, "Synthesis of Improved Zero-Impedance Converter", December 1989. It is therefore an object of the present invention to provide a synthesis method to produce infinite disturbance rejection ratio and zero-order dynamics in electric motor drive systems with any kind of motor including dc, synchronous and asynchronous ac, and step motors, and with both position and velocity loop closed. As it will be shown in the detailed description, the algorithms that hold for the preferred embodiment of the present invention are thus independent of a combined transfer function of a stabilizing and control circuit located in a forward path of the embodiment. Briefly, for use with an electric motor drive system, the preferred embodiment of the present invention includes a positive current feedback loop within a negative position and velocity feedback loops, and further includes control functions in a direct paths with respect to both position and velocity feedback loop and in a feedforward path. The positive current feedback loop comprises a current feedback circuit whose transfer function is H(s) given as
H(s)=Z where Z The control function in direct path with respect to the position feedback loop is implemented as a position direct path circuit characterized by a gain constant
K where m is a constant providing scaling between input and output of the system, i.e., the system transfer function becomes equal to m, K The control function indirect path with respect to the velocity feedback loop is implemented as a velocity direct path circuit characterized by a gain constant
K where K The control function in the feedforward path is implemented as a feedforward circuit characterized by a gain constant
K where K The positive current feedback incorporating the current feedback circuit of transfer function H(s) of Eq.(1), forces the motor impedance to zero yielding a load independence, i.e., an infinite disturbance rejection ratio, and further reduces the order of a system transfer function. The system transfer function is then brought to a zero-order function, i.e., constant m, for the control functions in direct paths and in feedforward path given in Eqs.(2), (3), and (4), respectively, yielding a zero-dynamics/instantaneous response with respect to an input command with associated zero error in both transient and steady state. Other advantages of the present invention include its ability to be realized in an integrated-circuit form; the provision of such a method which provides independence on a transfer function of a circuits located in a forward path of the embodiment; the provision of such a method which provides zero output-angular-velocity/position-change-to-load-torque-change transfer function in both steady state and transient; and the provision of such a method which provides constant output-angular-velocity/position-change-to-input-command/reference-change transfer function in both steady state and transient. As indicated in Eq.(1), the circuit realization of the current feedback circuit in the positive current feedback loop is a direct and explicit function of the impedance of an electric motor, Z The algorithm of Eq.(1) operates independently of an equivalent circuit of electric motor (the equivalent circuit incorporating mechanisms of producing both torque and back emf in the motor); it uses only information about the motor equivalent impedance, Z These and other objects and advantages of the present invention will no doubt be obvious to those skilled in the art after having read the following detailed description of the preferred embodiment which is illustrated in the FIGURE of the drawing. FIG. 1 is a block and schematic diagram of the preferred embodiment of the invention. An electric motor drive system embodying the principles of the invention whereby featuring an infinite disturbance rejection ratio and zero-dynamics/instantaneous response is shown in FIG. 1. In FIG. 1, it is assumed that input voltage V The embodiment in FIG. 1 employs a positive current feedback loop within a negative feedback velocity and position loops and further employs a control functions in a direct paths with respect to both position and velocity feedback loop and in a feedforward path. The positive current feedback loop incorporates a current feedback circuit 116 whose transfer function is H(s). Either analog or digital (microprocessor) realization of the current feedback circuit 116 may be done. The purpose of the positive current feedback loop is to make the system of infinite disturbance rejection ratio, i.e., to provide load independence, which it does for the transfer function H(s) synthesized as given in Eq.(1)and shown in FIG. 1 as it will be explained shortly. The purpose of negative velocity and position feedback loops is to stabilize the system and control its dynamics by means of a stabilizing network 144 and a control block 145. Another purpose of the two negative feedback loops is to provide(varying) dc feedback voltages in closing the loops, i.e., on leads 126 and 141, without additional filtering necessary, for example, in cases in which a negative voltage feedback loop is closed taking the PWM voltage supplied to the motor ΔV(s) and feeding it back in a negative loop. Although the position and velocity feedback loops then require appropriate feedback sensing devices, e.g. digital encoder and tach, they further provide a benefit of independence of the algorithms of the embodiment, given in Eqs.(1)through (4), of a combined transfer function of the circuits located in the forward path of the system, i.e., of the circuits 144 and 145 whose individual transfer functions are G The control function in direct path with respect to the position feedback loop incorporates a position direct path circuit 133 of a constant gain K In operation, the current ΔI(s) through an electric motor impedance 110 of value Z A number of pulses corresponding to the position error is supplied by lead 136 to a D/A converter 138 whose gain is K The voltage representative of a motor current, RΔI(s), is buffered by a differential amplifier 112 whose gain constant is K. The output of the isolating/buffering amplifier 112 is connected via lead 113 to a current feedback circuit 116 whose transfer function is H(s). The current sense signal obtained and processed in this way is then added in summer 102 in the positive feedback manner via lead 103 to the control signal ΔV.sub.Δl (s), available on lead 101, and to the feedforward signal, available on lead 143. The resulting total control signal, obtained by summing in the positive feedback manner the current sense signal, processed by the current feedback circuit 116, with both control and feedforward signal, is applied by lead 104 to a pulse width modulation (PWM) control circuit 105 which in turn controls and drives a PWM power stage 106. The combined voltage gain of control stage 105 and power stage 106 is a constant Thus, a voltage ΔV(s) is applied via lead 107 to the motor creating motor current ΔI(s) through the motor equivalent impedance Z The implementation of the PWM control 105 and power stage 106 is irrelevant for the functioning of the preferred embodiment of FIG. 1. It is only the overall voltage gain A of these two blocks which is involved in the algorithms of the preferred embodiment of FIG. 1. It is understood that signals associated with the summing circuit 102 are compatible in that they are: a dc varying signals in case of a dc motor; a sinusoidal signals of the same frequency in case of an ac motor; and a pulse signals of the same rate in case of a step motor (which produces an angular shaft speed Δω The scaling factor m in blocks 133, 129, and 142 has units in [radian/Volt] for a voltage command ΔV The electric motor equivalent impedance 110 is a series connection of a resistance R
Z while in case of an asynchronous ac (induction) motor the equivalent impedance 110 is a series connection of a stator impedance (R
Z The dynamic stiffness of the system of FIG. 1 is, for R<<|Z
-ΔT
where
T
T
T
T The transfer function of the preferred embodiment of FIG. 1, for R<<|Z
Δθ
where
T
T Denoting a part of the output angular shaft position response due to the input position command in Eq.(12) Δθ
D Combining Eqs.(15) and (10) it is seen that for the transfer function of the current feedback circuit as given in Eq.(1)and repeated here
H(s)=Z the disturbance rejection ratio becomes infinite, i.e.,
D In addition to providing an infinite disturbance rejection ratio, the algorithm of Eq.(16) reduces the order of the system transfer function originally given in Eq.(12), as seen by substituting Eq.(16) into Eq.(10) and then Eq.(10) into Eq.(9) so that T
Δθ
where
G
τ
T From Eq.(18) the zero dynamics is achieved for
τ which implies that time constant τ
K in which case the system transfer function of Eq.(18) becomes
Δθ The condition for zero dynamics, as given in Eq.(23), can be resolved in two independent conditions, one for position and another for velocity loop, by synthesizing the respective gain constants as given in Eq.(2) and here
K
and
K in which case Eq.(24) becomes
Δθ The zero-order dynamics provided in Eq.(27) implies instantaneous response to an input command with associated zero error in both transient and steady state. The condition in Eq.(26) is simply implemented, with reference to the system block diagram in FIG. 1 and remembering that it was derived for K
K and by implementing the feedforward circuit 142 such that it is characterized by a gain constant given in Eq.(4) and here
K The condition in Eq.(16) therefore provided for infinite disturbance rejection ratio, resulting into Eq.(17), and the conditions in Eqs.(16), (25), (28) and (29) provide for zero-dynamics/instantaneous response, resulting into Eq.(27). It is well known in classical control theory that both properties claimed above, i.e., an infinite disturbance rejection ratio and a zero-order dynamics with associated instantaneous response, can be achieved only for an infinite loop gain in the system of interest, i.e., by providing a block of infinite gain topologically located in the loop before the point of entry of disturbance. However, long before approaching any infiniteness in its loop gain such a system would become unstable and therefore useless. The instability is due to nonzero time constants, associated with the plant, i.e., the object of control, which cause phase shifts which at some frequencies will accumulate so that, together with a 180° phase shift in a negative feedback loop, the total phase shift will equal 360°=0° which, for loop gains greater than one, creates unstable system. In modern control theory the problem basically remains the same. We will cite at this point a portion of a paragraph from the book "Feedback Control Systems" by Charles L. Phillips and Royce D. Harbor, Prentice Hall, 1988. specifically from section "Pole-Placement Design" dealing with the concluding remarks on page 518. The citation is: "It appears from the preceding example that we can choose the magnitude of the real part of the roots arbitrarily large, making the system response arbitrarily fast. For the system model, we can do this. However, as the time constant of the system becomes smaller, the gains increase. This is true, in general, since to increase the rate at which a plant responds, the input signal to the plant must become larger". The preferred embodiment of the present invention, as well as patents and copending and coassigned applications, in their own application domains, by these two same inventors, as stated in the background of the invention, works in such a way as to force all system time constants to zero while providing a finite loop gain ensuring a complete stability and achieving ideal properties given in Eqs.(17) and (27). Actually, the embodiment of FIG. 1 possesses a block in the loop which features an infinite gain but the total loop gain is finite! To visualize this better, we shall notice that a transadmittance ΔI(s)/ΔV.sub.ε1 (s), as a function of interest here, is obtained from FIG. 1 as
ΔI(s)/ΔV.sub.ε1 (s)=A/{(Z while a transfer function Δω
Δω It is then seen that by substituting the algorithm given in Eq.(16) into above two expressions the transadmittance part due to impedance [Z
Δω It is therefore clear that any loop gain in the system of FIG. 1 is finite but, at the same time, the system is completely free of any time constants associated with both electric motor impedance Z Returning to the citation presented earlier, in which it is said that "as the time constant of the system becomes smaller, the gains increase", we note that the preferred embodiment of the present invention in FIG. 1 reduces system time constants exactly to zero while providing quite finite loop gains; the velocity loop gain and the position loop gain being
LG
and
LG respectively, so that transfer function G The embodiment of FIG. 1 performs in such a way as to be limited only by the physics limitations such as finite energy level of available sources, finite power dissipation capability of available components, and finite speed of transition of control signals. With regards to a circuit realization of the block 116 in the positive current feedback loop, it is seen from Eqs.(5) and (16) that this block is realized by implementing a differentiator circuit with a dc path in case of dc, synchronous ac, and step motors, while in case of asynchronous ac (induction) motors the circuit realization of block 116 is done in accordance with Eqs.(6) and (16). Therefore, the circuit realization of block 116 is simple and exactly determined by Eqs.(5), (6), and (16). Alternatively, a software implementation, based on implementing Eqs.(5), (6), and (16), can be done in order to realize block of transfer function H(s). As with reference to realizing the other three algorithms of the preferred embodiment of FIG. 1, i.e., the position direct path circuit 133 characterized by a gain constant of Eq.(25), the velocity direct path circuit 129 characterized by a gain constant of Eq.(28), and the feedforward circuit 142 characterized by a gain constant of Eq.(29), they are realized by implementing a constant gain circuits in accordance with Eqs.(25), (28), and (29). Various changes and modifications may be made , within the scope of the inventive concept without departing from it. For example, only velocity feedback may be employed and the same properties of the embodiment are preserved using algorithms in Eqs.(16),(positive current feedback is always employed), (28), and (29). In another example, the algorithms in Eqs.(28) and (29) are implementable as well by implementing Eq.(26). In yet another example, if the back emf mechanisms are characterized by a more complex function than the constant K Also, the conceptual employment of the scaling constant m in both position and velocity direct path circuits 133 and 129, and in the feedforward circuit 142, producing for the system transfer function the constant m, as given by Eq.(27), may not be feasible in practical terms in cases in which this employment would cause voltage levels in the signal portion of the system higher than normally assumed, i.e., voltages at the outputs of blocks 133, 129, and 142 would be, in those cases, higher than normally expected. This problem is easily solved by moving the scaling constant m from blocks 133, 129, and 142 to the pulse width modulation power stage 106, where the voltage levels can assume the expected values. In order for this to be done, the loop gains involving the voltage gain of the PWM control and power stage must, of course, be kept the same. This is easily done by dividing gain constant of block 112 with m, if the gain constant A is to be multiplied by m. Therefore, in such a case, the preferred embodiment of FIG. 1 may easily be changed, without affecting any of the properties obtained here, to accommodate for reasonable voltage levels in the signal and control portion of the system, by: changing gain of the position direct path circuit 133 from K Patent Citations
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